Thixotropic Yield Stress Fluids Research Articles

Interplay between wall slip and shear banding in a thixotropic yield stress fluid.

We study the local dynamics of a thixotropic yield stress fluid that shows a pronounced non-monotonic flow curve. This mechanically unstable behavior is generally not observable from standard rheometry tests, resulting in a stress plateau that stems from the coexistence of a flowing band with an unyielded region below a critical shear rate c. Combining ultrasound velocimetry with standard rheometry, we discover an original shear-banding scenario in the decreasing branch of the flow curve of model paraffin gels, in which the velocity profile of the flowing band is set by the applied shear rate  instead of c. As a consequence, the material slips at the walls with a velocity that shows a non-trivial dependence on the applied shear rate. To capture our observations, we propose a differential version of the so-called lever rule, describing the extent of the flowing band and the evolution of wall slip with shear rate. This phenomenological model holds down to very low shear rates, at which the dimension of the flowing band becomes comparable to the size of the individual wax particles that constitute the gel microstructure, leading to cooperative effects. Our approach provides a framework where constraints imposed in the classical shear-banding scenario can be relaxed, with wall slip acting as an additional degree of freedom.

Theoretical study on Poiseuille flow of thixotropic yield stress fluids: an exact solution

Theoretical study on Poiseuille flow of thixotropic yield stress fluids: an exact solution

Unification of rheology of thixotropic yield stress fluids and screen printing properties of pastes

At present, the electrode width of solar cells has been successfully reduced to less than 20 µm. Ensuring its morphology and aspect ratio remains a major challenge to further reducing the electrode width, which puts higher requirements on the performance of the paste. Previous studies have focused less on selecting organic carrier components and the relationship between carrier and paste printing suitability. Therefore, in this study, considering the wettability of the solvent to the silicon wafer, the solubility to the binder and the boiling point, the selection method of the mixed solvent for the organic carrier was given. The Herschel-Buckley model was introduced to characterize the flow behavior of the organic carrier. Furthermore, the model parameters were unified with the printability of the paste and the organic carrier model parameters corresponding to the paste with good printability were contributed. The results showed that when the consistency index (K) was 21.883 and the exponent (n) was 0.1545, the aspect ratio of the electrode was the largest. When the yield stress (5.38 Pa) and thixotropic loop area (707.71 Pa s−1) were the largest, the morphology of the electrode was the most regular.

The effect of thixotropy on the yield transition in reversible, colloidal gels.

Thixotropic yield-stress fluids (TYSFs) are a unique class of materials whose properties are affected by both shear rate and shear history. When sheared, these materials undergo a transition from an elastic solid to a viscoelastic fluid, which is accompanied by a structural transition that slowly recovers upon the cessation of shear. The strong interdependence between structure, dynamics, and rheological properties in TYSFs make it challenging to identify the fundamental physics controlling these phenomena. In this study, we vary the ionic strength of a suspension of cellulose nanocrystals (CNC) to generate model TYSFs with tunable moduli and thixotropic kinetics. We use a novel rheological protocol-serial creep divergence-to identify the physics underlying the yield transition and recovery of CNC gels. Our protocol identifies a critical transition that bifurcates the solid-like and fluid-like regimes of the gels to precisely determine the yield stress of these materials even in the presence of thixotropic effects. Additionally, the thixotropic kinetics collapse onto a single master curve, which we fit to a transient solution to a coupled diffusion-aggregation model. Our work thereby identifies the underlying physicochemical mechanisms driving yielding and thixotropic recovery in attractive colloidal gels.

Stick-slip behavior of a clayey crustal fault

Recent studies have revealed that slip on clay-rich fault planes, which develop in the shallow crust and can cause huge earthquakes, is controlled by their flow properties rather than their frictional properties. Here, we simulate a seismogenic crustal fault and show that such a fault plane may behave as a thixotropic yield stress fluid. We then conduct numerical experiments using a simple spring-slider model that incorporates this thixotropic property, and we successfully reproduce spontaneous stick-slip behaviors that correspond to a variety of seismogenic processes, ranging from regular earthquakes with high slip rates to slow earthquakes with lower slip rates. This finding suggests that the seismic activity on a shallow clay-rich crustal fault may be governed by the time-evolving microstructure of the clay-water system that exists along the fault plane.

Nonlocal effects in the shear banding of a thixotropic yield stress fluid

A simple analytical model is introduced for describing the combined effect of thixotropic and nonlocal flow in a homogeneous stress field. The model adequately describes experimental rheo-MRI velocimetry profiles, measured for a milk microgel suspension in a cone-and-plate geometry.

Rheological characterization of flow inception of thixotropic yield stress fluids using vane and T-bar geometries

Rheological characterization of flow inception of thixotropic yield stress fluids using vane and T-bar geometries

Yielding, thixotropy, and strain stiffening of aqueous carbon black suspensions

We study experimentally the rheological behavior of carbon black (CB) suspensions in water at different ionic strengths and concentrations. We show by means of standard rheometry completed by local magnetic resonance imaging-rheometry that these suspensions first appear to be thixotropic yield stress fluids: they exhibit a yield stress increasing with the time of rest, their apparent viscosity decreases under shear, and a viscosity bifurcation occurs around the yield stress, the fluid evolving either towards stoppage or to steady flow at a large shear rate for a small stress change. Then, an original effect appears when we follow the mechanical state of the material in the solid regime by measuring its apparent elastic modulus at small deformation during a creep test under various stresses. In contrast with various other yield stress fluids for which the elastic modulus under small deformation appears to be constant for any deformation in the solid regime, for CB suspensions, this modulus widely increases while deformation increases up to yielding. We suggest that this strain stiffening effect finds its origin in the specificities of the (van der Waals) interactions and of the (rough) structure (aggregates) of the particles: the slight relative rotation of particles in contact due to deformation would, on average, tend to increase the net area of contact between particles, which stiffens the whole material structure. This is supported by the observation that the relative increase of elastic modulus is approximately proportional to sample deformation, whatever the material characteristics (ionic strength, concentration) and whatever the deformation history.

A thermodynamic framework for modelling thixotropic yield stress fluids: Application to cement pastes

In this paper, a Helmholtz-potential-based thermodynamic approach was developed for modelling fluids that exhibit both yielding and thixotropic behavior. The yielding behavior was captured using a framework of multiple natural configurations. The thixotropy was described using a structural parameter. The Helmholtz potential is made a function of a structural parameter and a stretch quantity, and the rate of dissipation was made to depend on the rate of change of the natural configuration and the time derivative of the structural parameter. The final constitutive equations were obtained by maximizing the rate of dissipation with the reduced dissipation equation as a constraint. For experimental corroboration of the model, steady-shear and step-shear experiments were performed using cement paste. The predictions from the model were found to match well with the experimental data. Finally, the different model variants that can also be obtained using the presented framework are discussed.

Letter to the Editor: Modeling the nonmonotonic time-dependence of viscosity bifurcation in thixotropic yield-stress fluids

Letter to the Editor: Modeling the nonmonotonic time-dependence of viscosity bifurcation in thixotropic yield-stress fluids

Time-dependent shear rate inhomogeneities and shear bands in a thixotropic yield-stress fluid under transient shear.

We study the rheological responses and shear-rate inhomogeneities and shear banding behaviors of a thixotropic fumed silica suspension in shear startup tests and flow reversal tests. We find that this suspension under transient shear exhibits not only viscoelasticity, yielding, kinematic hardening, and thixotropy, but also time-dependent shear inhomogeneities including bands when the apparent shear rate is below a critical value between 0.1 and 0.25 s-1. Through multiple shear startup tests and flow reversal tests, we find that thixotropy promotes flow heterogeneity while kinematic hardening suppresses it. We propose a simple thixo-plastic constitutive equation that can qualitatively predict the important features of the rheological response and banding dynamics in shear startup tests and flow reversal tests.

Carbopol: From a simple to a thixotropic yield stress fluid

There is an ongoing discussion in the literature about the flow behavior of the widely used model yield-stress fluid Carbopol. Some papers show that it is indeed the simple model yield-stress fluid that many people believe it to be. However, other authors report rheological hysteresis in the flow curve, transient shear banding that persists for a very long time, and the breaking of fore-aft symmetry in a falling ball experiment. Such behaviors have in the past been associated with thixotropic yield stress fluids, which are very different from simple ones. We present experiments that suggest that both types of behavior may be found in the same type of Carbopol, depending on the preparation: After strong stirring for a long time, the system becomes slightly thixotropic. Flow visualization experiments with fluorescently labeled Carbopol elucidate the difference between the simple and thixotropic behavior of the systems: The stirring breaks the polymers into smaller fragments, some of which are so small that they exhibit Brownian motion. We propose that this generates a depletion interaction that leads to gel formation, which in turn leads to the thixotropy.

A singular perturbation study of the Rolie-Poly model

A singular perturbation analysis for the Rolie-Poly model is presented for the limit of large relaxation time. The model describes entangled linear polymer melts and time scales for a Rouse time and reptation time. First, the case of the Rouse time approaching zero is named the nonstretching model, and the addition of a solvent model gives the small parameter to be the ratio of the retardation time to the slow reptation time. This analysis is instructive in formulating the perturbation analysis for the full Rolie-Poly model without the solvent, where the small parameter is the ratio of Rouse time to reptation time. The resulting formulae elucidate the characteristic features of thixotropic yield stress fluids, including yield stress hysteresis, delayed yielding and long term persistence of a decreased viscosity after cessation of flow. Two fundamental initial value problems are solved: startup of shear flow and cessation of shear flow. The scalings lead naturally to simplified dynamical systems that describe regimes of fast, slow and yielded dynamics, and show how the combination of these regimes can be used to describe the entire flow evolution.

Quasi-periodic and irregular motion of a solid sphere falling through a thixotropic yield-stress fluid

We report the observation of the oscillatory and irregular motion of solid spheres settling under the influence of gravity in a thixotropic yield-stress fluid, namely, a suspension of Laponite. The size of the ball and the aging time of the Laponite suspension are found to be two important parameters that determine whether oscillations occur. The irregular motion may be related to the existence of an unstable flow region and shear banding as is concluded from comparisons with rheological measurements, namely, the flow curve and creep tests, using the same Laponite suspensions.

Stability of shear banded flow for a viscoelastic constitutive model with thixotropic yield stress behavior

A viscoelastic constitutive model which combines the partially extending strand convection model and a Newtonian solvent is used in the regime of large relaxation time. Prior work on one dimensional time-dependent solutions at prescribed shear stress predicts some of the features expected of thixotropic yield stress fluids, such as delayed yielding. In this paper, we present the linear stability analysis of two-dimensional plane Couette flow, for parameter regimes that support a two-layer arrangement consisting of an unyielded layer and a yielded layer. Asymptotic analysis and computational techniques are applied. We find that the one layer yielded flow can have bulk instabilities which also emerge in the two-layer flow. Bulk instabilities in the yielded phase appear not to have been observed in prior literature. For some parameters, an interfacial mode is unstable and is driven by the normal stress difference across the interface. The yielded zone has the higher first normal stress difference, as for the well-studied Johnson–Segalman model. In order to assess the importance of the sign of the first normal stress difference at the interface, we specifically design a modification to the model to reverse the sign. It is found that instabilities still occur.

Taylor-Couette instability in thixotropic yield stress fluids

In the present work, we study the flow of thixotropic yield stress fluids between two concentric cylinders. In order to take into account the thixotropy, the constitutive relation uses a structural parameter which is driven by a kinetic equation. Here, the Houska's model is considered. Depending on the breakdown rate of the structural parameter, localization or shear-banding are observed. We show that for fragile structures, a shear-banding flow may be observed although for stronger structures, only localisation of the flow is observed such as in Bingham fluids. Physical explanations of the shear-banding discussed by several authors in the literature highlight that the shear-banding may be associated with a discontinuity into the structure of the material and a non-monotonic evolution of the stress according to the constitutive relation with the strain rate. Solving numerically the flow, we show that such a rheological model based on the existence of a structural parameter is able to predict shear-banding. Moreover, the consequences of the thixotropy on the linear stability of the azimuthal flow is studied in a large range of parameters. Although the thixotropy allows shear banding for the base flow, it does not modify fundamentaly the stability of the Couette flow compared to a simple yield stress fluid. The apparent shear-thinning behaviour depends on the thixotropic parameters of the fluid and the results about the onset of the Taylor vortices in shear-thinning fluids are retrieved. Nevertheless, the shear-banding modifies the stratification of the viscosity in the flowing zone such that the critical conditions are mainly driven by the width of the flowing region.

Shear-banding predicted by a constitutive model with a structural parameter in cylindrical Couette flows

Dense suspensions of non-Brownian particles may partially behave as thixotropic yield stress fluids. We study the flow of such fluids between two concentric cylinders using a phenomenological structural kinetics model. The structural kinetics approach balances the simplicity of phenomenological continuum approaches with a simplified model for structure against the complexity a more fundamental model based on particle micromechanics. A modified version of Houska’s model, which includes a diffusive term for the structural parameter, is considered. Depending on the breakdown rate of the structural parameter, shear-banding may be observed. For shear-banding in steady flows, the stress selection depends on the diffusion of the structural parameter. If there is no structural diffusion, the displacement of the interface between the flowing and the static regions fixes the stress at the interface during the transient flow. In the cases of very small diffusive coefficients, the stress at the fluid / solid interface converges to a limit value which is different from the yield stress of the structured material as expected without any diffusion. Nevertheless, the inner torque and the flow profile are quite similar in both cases and the differences are localized near the fluid / solid interface. For shear-banding, the gradients of the structural parameter and the strain rate are very abrupt but the continuity is preserved by the diffusion.

Evolution of strength and failure of SCC during early hydration

The early strength evolution of self-consolidating concrete (SCC) is studied by a set of non-standard mechanical tests for compressive, tensile, shear and bending failure. The results are applicable in an industrial environment for process control, e.g. of slip casting with adaptive molds in robotic fabrication. A procedure for collapsing data to a master evolution curve is presented that allows to distinguish two regimes in the evolution. In the first, the material is capable of undergoing large localized plastic deformation, as expected from thixotropic yield stress fluids. This is followed by a transition to cohesive frictional material behavior dominated by crack growth. The typical differences in tensile and compressive strength of hardened concrete are observed to originate at the transition. Finally, the evolution of a limit surface in principal stress space is constructed and discussed.

Thixotropy in yield stress fluids as a limit of viscoelasticity

[Received on ] Thixotropic yield stress fluids have a yield stress and viscosity which change slowly over time as the fluid undergoes structural changes. This article reviews recent work which shows how such behavior can arise as a limit of viscoelastic flow when a relaxation time becomes large. The large relaxation time introduces a small parameter which can be used as a basis for singular perturbation studies. A simple prototype for a viscoelastic model will be used to illustrate the analysis. We review the behavior in startup of shear flow, oscillatory shear flow and elongational flow and identify potential directions for future research.

Yielding and flow of cellulose microfibril dispersions in the presence of a charged polymer.

The shear flow of microfibrillated cellulose dispersions is still not wholly understood as a consequence of their multi-length-scale heterogeneity. We added carboxymethyl cellulose, a charged polymer, that makes cellulose microfibril dispersions more homogeneous at the submicron and macro scales. We then compared the yielding and flow behavior of these dispersions to that of typical thixotropic yield-stress fluids. Despite the apparent homogeneity of the dispersions, their flow velocity profiles in cone-plate geometry, as measured by rheo-MRI velocimetry, differ strongly from those observed for typical thixotropic model systems: the viscosity across the gap is not uniform, despite a flat stress field across the gap. We describe these velocity profiles with a nonlocal model, and attribute the non-locality to persistent micron-scale structural heterogeneity.